Quarterly data for the period 1960: 1 to 1997: 2, conventional tests, a bootstrap simulation approach and a multivariate Rao&#39;s F-test have been used to investigate if the causality between government spending and revenue in Finland was changed at the beginning of 1990 due to future plans to create the European Monetary Union (EMU). The results indicate that during the period before 1990, the government revenue Granger-caused spending, while the opposite happened after 1990, which agrees better with Barro&#39;s tax smoothing hypothesis. However, when using monthly data instead of quarterly data for almost the same sample period, totally different results have been noted. The general conclusion is that the relationship between spending and revenue in Finland is still not completely understood. The ambiguity of these results may well be due to the fact that there are several time scales involved in the relationship, and that the conventional analyses may be inadequate to separate out the time scale structured relationships between these variables. Therefore, to investigate empirically the relation between these variables we attempt to use the wavelets analysis that enables us to separate out different time scales of variation in the data. We find that time scale decomposition is important for analysing these economic variables.

The properties of the Granger-causality test in stationary and stable Vector Autoregressive (VAR) models are studied with different types of volatility processes imposed on the unconditional variance. For this test, it is examined how the size and power properties are affected by different magnitudes of GARCH processes and by structural shifts in the volatility. The study has been conducted by means of Monte Carlo simulations for different sample sizes. Our analysis reveals that substantial GARCH effects influence the size properties of the Granger-causality test, especially in small samples. The power functions of the test are usually slightly lower in the presence of GARCH disturbances compared to the case of white noise residuals. When a structural variance break is imposed, the size problem is rather severe, and the power functions are lower compared to the case with the pure GARCH processes.

By using bootstrap technique we investigate the properties of the Breusch [Breusch, T.S., 1978. Testing for autocorrelation in dynamic linear models. Australian Economic Papers 17, 334–355]–Godfrey [Godfrey, L.G., 1978. Testing for higher order serial correlation in regression equations when the regressors include lagged dependent variables. Econometrica 46, 1303–1310] autocorrelation tests in dynamic models with uncorrelated but not independent errors. In this paper we show that, under conditions when the errors are uncorrelated but not independent, even the best likelihood ratio test cannot achieve the asymptotic distribution under the null hypothesis of no autocorrelation. Standard bootstrap methods also fail to produce consistent results. To overcome this problem we applied several bootstrap testing methods for the same purpose and found the stationary bootstrap and Wild bootstrap with static model to perform adequately among the other bootstrap methods.

In systems ranging from 1 to 10 equations, the size and power of various generalization of the Regression Specification Error Test (RESET) test for functional misspecification are investigated, using both the assymptotic and the bootsrap critical values. Furthermore, the robusteness of the RESET test to various numbers of non-normal error terms has been investigated. The properties of eight versions of the test are studied using Monte Carlo methods. Using the assyptotic critical values together with normally distributed error terms,we find theRao’smultivariate F-test to be best among all other alternative testmethods (i.e.Wald, Lagrange Multiplier and Likelihood Ratio). In the cases of heavy tailed error terms, short or long tailed errors, however, the properties of the bestRao test deteriorates especially in larg systems of equations.By using the bootstrap critical values, we find that the Rao test exhibits correct size but still slightlyunder reject the null hypothesis in cases when the error terms are short tailed. The powerof the test is low, however, in small samples and when the number of equations grows.

The size and power of various generalization of the RESET test for functional misspecification are investigated, using the “Bootsrap critical values”, in systems ranging from one to ten equations. The properties of 8 versions of the test are studied using Monte Carlo methods. The results are then compared with another study of Shukur and Edgerton (2002), in which they used the asymptotic critical values instead and found that in general only one version of the tests works well regarding size properties. In our study, when applying the bootstrap critical values, we find that all the tests exhibits correct size even in large systems. The power of the test is low, however, when the number of equations grows and the correlation between the omitted variables and the RESET proxies is small.

Using Monte Carlo methods, the properties of systemwise generalizations of the Breusch Godfrey test for autocorrelated errors are studied when there are some kinds of GARCH effects among the errors. The analysis, regarding the size of the test, reveals that the GARCH have considerable effects of the properties of the test regarding the size, especially in large systems of equations. The corrected LR tests, however, have been shown to perform satisfactorily in small systems when the errors are white noise or they have low GARCH effects, whilst the commonly used TR2 test behaves badly even in single equations. All tests perform badly, however, when the number of equations increases and the GARCH effect is strong. As regards the power of the test, the GARCH was not found to have any significant effects on the power properties of the test.

The RESET test for functional misspecification is generalised to cover systems of equations, and the properties of 7 versions are studied using Monte Carlo methods. The Rao F -test clearly exhibits the best performance as regards correct size, whilst the commonly used LRT (uncorrected for degrees-of-freedom), and LM and Wald tests (both corrected and uncorrected) behave badly even in single equations. The Rao test exhibits correct size even in ten equation systems, which is better than previous research concerning autocorrelation tests. The power of the test is low, however, when the number of equations grows and the correlation between the omitted variables and the RESET proxies is small.